First substitute the values for 1970 into the equation. In 1970, t
= 0, and A = 10,000

10,000 = Per(0)

10,000 = Pe0

But anything to the 0th is 1 so we get

10,000 = P

The initial amount is the y intercept.

NOw that we know P, we can substitute our values for 1990 into the
equation. In 1990, t = 20 and P = 50,000

50,000 = 10,000er(20)

Divide both sides by 10,000

5 = e20r

Take natural logs of both sides

ln 5 = 20r

Divide both sides by 20

ln 5 is approximately 1.6094, so the answer is approximately

r = 0.08047

This gives us our equation

A = 10,000e0.08047t

b) With this formula we can predict the population in 2000. In
2000, t will be 30

A = 10,000e0.08047(30)

A = 10,000e2.414

A = 111,785

Since we are using decimal approximations, you will probably get a
slilghtly different answer if you round off differently than was done
here. Our calculations used numbers which were rounded off to 4
significant digits, so the correct answer should be